How can basic research on mathematics instruction contribute to instructional improvement? In our research on the practical rationality of geometry teaching we describe existing instruction and examine how existing instruction responds to perturbations. In this talk I consider the proposal that geometry instruction could be improved by infusing it…

The educational project "From Soccerene to Fullerene" (FSTF) was a pioneering interdisciplinary experience accomplished by six pupils who discussed it in the 2013 Italian school-leaving examination. The author illustrated the FSTF in the 2014 national conference of the Italian Physical Society (Pisa) eliciting a genuine interest. Here we…

To deepen our understanding of those aspects of problems that cause the most difficulty for solvers, this study integrated eye-tracking with handwriting devices to investigate problem solvers' online processes while solving geometry problems. We are interested in whether the difference between successful and unsuccessful solvers can be identified…

The purpose of this paper is to provide examples of "non-traditional" proof-related activities that can explored in a dynamic geometry environment by university and high school students of mathematics. These propositions were encountered in the dynamic geometry environment. The author believes that teachers can ask their students to…

This article argues that mathematical knowledge, and its related pedagogy, is inextricably linked to the tools in which the knowledge is expressed. The focus is on digital tools and the different roles they play in shaping mathematical meanings and in transforming the mathematical practices of learners and teachers. Six categories of digital…

According to the constructivist approach in mathematics education, knowledge is actively created or invented by the students, not passively received from the teacher or the environment. In this regard, learning environments should be designed so that students have to use effectively their "own" knowledge and thus students achieve desired…

Developing students' geometric reasoning skills is dependent on the quality of task designs and the role of the teacher. The purpose of this study was to apply Sfard's (2008) interpretive framework to analyse changes in students' mathematical discourse. This paper reports on the results of an investigation into the ways one class of Year 7…

This paper reports on a project aimed at developing a system of professional support for the improvement of the Geometry for Teachers course that mathematics departments teach to preservice secondary teachers. We share data from interviews with 20 instructors to report on how they perceive their position of geometry instructors and the work they…

As a parent, the author stepped into his child's class on a Friday morning to a room buzzing with activity. Parents walked around the room, coffee and bagel in hand, reading stories that their child (and others) had drafted, revised, written, and illustrated. Students eagerly shared their stories and drawings, cherishing the comments and praise…

GeoGebra is a free tool that has the potential to change both how and what is taught in mathematics. GeoGebra allows teachers and students to explore various mathematical ideas either through the full applet (https://www.geogebra.org/graphing) or by sharing applets via GeoGebra's Materials site (https://www.geogebra. org/materials/). It has many…

The aim of this study is to examine the mathematical creativity of individuals who think they have creative thinking skills. Forty-four teachers who work in private schools participated in this study and they have their pedagogical formation training from a public university in order to be a public teacher. Also participants have at least one year…

Educational modules can play an important part in revitalizing the teaching and learning of complex analysis. At the Westmont College workshop on the subject in June 2014, time was spent generating ideas and creating structures for module proposals. Sharing some of those ideas and giving a few example modules is the main purpose of this paper. The…

The objective of this present research is to analyze the implementation of learning geometry through a scientific learning consisting of three aspects: 1) teacher's activities, 2) students' activities and, 3) the achievement results. The adopted approach is a descriptive-quantitative one and the subject is the Class VII students of Islamic Junior…

This study investigates three teachers' uses of a dynamic geometry program (The Geometer's Sketchpad) in their high school geometry classes over a 2-year period. The researchers examine teachers' actions and questions during pivotal teaching moments to characterize mathematics instruction that utilizes technology. Findings support an association…

The classical "brachistochrone" problem asks for the path on which a mobile point M just driven by its own gravity will travel in the shortest possible time between two given points "A" and "B." The resulting curve, the cycloid, will also be the "tautochrone" curve, i.e. the travelling time of the mobile…